UAV-assisted federated learning resource allocation method

Abstract

The present application provides an unmanned aerial vehicle (UAV)-assisted federated learning resource allocation method for an UAV-assisted federated learning wireless network scenario, which takes into account the effect of altitude of the UAV on the coverage range in order to achieve an equilibrium between the total energy consumption of the user and federated learning performance. The method simultaneously considers the total energy consumption of the user and the federated learning performance, defines the total cost function of the system. The total cost function consists of weighting of the total energy consumption of the user and the inverse of the number of users participating in federated learning, and forms the optimization problem with a minimization of the total cost function.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Chinese Patent Application No. 202310113221.9, titled “UAV-assisted Federated Learning Resource Allocation Method”, filed Feb. 15, 2023, the entire disclosure of which is incorporated herein by reference.

TECHNICAL FIELD

The present application relates to the field of communication technology, and specifically relates to an UAV-assisted federated learning joint learning performance and resource allocation method.

BACKGROUND

In recent years, the popularity of smart devices and the increasing scale of the Internet of Things (IoT) have led to an exponential growth in the amount of data. By analyzing and processing these data, some smart applications (face recognition, smart driving, voice recognition) have been developed at light speed, but they have also given rise to the issue of data security and privacy. With the gradual concern about privacy, more and more entities begin to emphasize the right of ownership and use of data, which reduces the data exchanges between different entities, and makes each entity gradually become a “data silos”. In order to solve the above problems, make greater use of the value of data, and improve the performance of AI algorithms, Federated Learning (FL) is emerged.

Federated Learning is able to coordinate all parties for joint learning without exposing the data of all parties, which improves the utilization of resources and guarantees the privacy of users compared with traditional centralized learning. In the process of federated learning, each participant does not need to upload the local raw data, but only needs to upload the neural network model parameters related to the data, and then the main server will securely aggregate the model parameters and feed them back to the participants, who will update the global model according to the dataset they own, which effectively ensures the security and privacy of sensitive data of each participant. In order to further improve the performance of federated learning, UAVs are beginning to be combined with federated learning as an airborne base station, and UAVs, as airborne mobile base stations, are able to quickly construct regional wireless networks and provide emergency communication services. Due to the combination of UAVs and federated learning, compared with the fixed base station scenario, UAVs can find a suitable position to reduce the energy consumption of the user, and to a certain extent alleviate the user's competition for wireless resources, and a reasonable resource allocation scheme can effectively reduce the energy consumption of the user, and enhance the efficiency of federated learning.

SUMMARY

The present application aims to propose an UAV-assisted federated learning resource allocation method. The method considers the influence of the flight altitude of the UAV on the coverage range and proposes a resource allocation mechanism to guarantee the learning performance while reducing the total energy consumption of the user.

To achieve the above functions, the present application designs an UAV-assisted federated learning resource allocation method, which constructs an optimization problem P with minimization of the total cost function, determines the optimal horizontal position decision of the UAV based on the user's state and the local accuracy, determines the optimal local accuracy based on the state of the UAV and the user, determines the optimal user resource allocation decision based on the position of the UAV and the local accuracy, and changes the flight altitude of the UAV, repeats the above steps to obtain the optimal altitude of the UAV to reduce the total energy consumption of the participating learning user.

In order to solve the above technical problems, the present application adopts the following technical program:

In a first aspect, the present application provides an UAV-assisted federated learning resource allocation method, including:

• • S1. determining a total cost function and constraints of a system based on total energy consumption of users that participate in the federated learning and an inverse of a number of the users, and constructing an optimization problem P with a minimization of the total cost function;
  • S2. solving by the optimization problem P to obtain an optimal horizontal position of the unmanned aerial vehicle (UAV) m, an optimal local accuracy, an optimal user resource allocation decision, and an optimal altitude of the UAV m; and
  • S3. the UAV m flying to the optimal horizontal position and the optimal altitude of the UAV m, and the users determine to participate in the federated learning within a coverage range of the UAV m based on the optimal user resource allocation decision and the optimal local accuracy.

In some embodiment, the S1, constructing the optimization problem P for minimizing the total cost function, includes:

• • S11. a set of users is denoted as Na=={1, 2 . . . N}, a set of the users within the coverage range of the UAV m is denoted as N_m; a distance between the user i and the UAV m is:
    d_im=√{square root over (h²+∥q_m−q_i∥₂²)};
  • where h denotes the altitude of the UAV m, q_m={x_m,y_m} denotes a horizontal position of the UAV m, q_i={x_i,y_i} denotes a position of the user i, and a channel gain of the user i is:

$g_i={g_0\left(\frac{d_{\mathrm{im}}}{d_0}\right)}^{-\alpha };$

• • where g₀ is a channel interference power at time d₀=1 m and α is a path loss exponent;

S12. energy consumption of the user's terminal during the federated learning comprises training energy and communication energy;

S13. Dⁱ denotes an amount of data of the user, f_i denotes a number of revolutions per second of a CPU of the user i, C_i denotes a number of revolutions of the CPU of the user i to process a sample data, and I_l denotes a number of rounds of local training when a local accuracy is achieved η;

$I_l=\frac{2}{\left(2-L\delta \right)\mathrm{\delta \gamma }}\log \left(\frac{1}{\eta }\right);$

• • wherein L, γ are relevant parameters about a neural network loss function, δ is a training learning step of the federated learning;
  • training energy consumption E_i^comp of the user i in one iteration of the federated learning is denoted as:
    E_i^comp=κI_lC_iD_if_i²;

S14. after the user i completes the local training, a trained model is uploaded to the UAV m by a frequency division multiple access (FDMA); b_i denotes a bandwidth allocated to the user i, p_i denotes a transmission power of the user i, N₀ denotes a noise power spectral density, and according to a Shannon's formula, an achievable transmission rate R_i of the user i is:

$R_i=b_i{\log }_2\left(1+\frac{g_i{p}_i}{N_0{b}_i}\right);$

• • assuming that a size of data of the neural network model w is s and communication energy consumption E_i^comm of the user i is:

$E_i^{comm}=p_i{t}_i=p_i\frac{s}{b_i{\log }_2\left(1+\frac{g_i{p}_i}{N_0{b}_i}\right)};$

• • S15. when a global model accuracy is required to be achieved ε₀, a number of communication rounds I_g is:

$I_g=\frac{2L^2}{{\gamma }^2\xi }\log \frac{1}{{\epsilon }_0}\frac{1}{1-\eta };$

• • where ξ denotes relevant parameters in a local neural network training, a total energy consumption E^total of a whole federated learning process is:

$E^{\mathrm{total}}=I_g\stackrel{❘N_m❘}{\sum _{i\in N_m}}\left(E_i^{comm}+E_i^{comp}\right);$

• • S16. the total cost function C is defined as:

$C=E_{\mathrm{total}}+\rho \frac{1}{N_m};$

• • a target function is:

$\underset{q_m,h,f,t,p,b,\eta }{\min }C=\underset{q_m,h,f,t,p,b,\eta }{\min }\frac{a}{\left(1-\eta \right)}\left(\sum _{i\in N_m}^{❘N_m❘}\log \left(\frac{1}{\eta }\right)v{C}_i{D}_i{f}_i^2+t_i{p}_i\right)+\frac{\rho }{N_m};$

• • wherein

$a=\frac{2L^2}{{\gamma }^2\zeta }\log \frac{1}{{\epsilon }_0}$
and

$v=\frac{2}{\left(2-L\delta \right)\mathrm{\delta \gamma }}$
denote fixed values and ρ denotes a weighting factor;

• • S17. considering the total energy consumption of the users and a performance of federated learning, the optimization problem P of the system is:

$\underset{q_m,h,f,t,p,b,\eta }{\min }\frac{a}{\left(1-\eta \right)}\left(\sum _{i\in N_m}^{\left|N_m\right|}\log \left(\frac{1}{\eta }\right)v{C}_i{D}_i{f}_i^2+t_i{p}_i\right)+\frac{\rho }{N_m};$

• • the constraints are:
    C1: 0≤f_i≤f_i^max
    C2: 0≤p_i≤p_i^max

$\begin{array}{cc}{I}_g\left(t_i+I_l\frac{C_i{D}_i}{f_i}\right)\le T& \mathrm{C3}\end{array}$ $\begin{array}{cc}{t}_i\ge \frac{s}{R_i}& \mathrm{C4}\end{array}$
C5: ∥q_m−q_i∥₂²≤r²
C6: h^min≤h≤h^max

$\begin{array}{cc}\sum _{i\in N_m}^{\left|N_m\right|}{b}_i\le B,b_i>0& C7\end{array}$
C8: 0≤η≤1;

• • where T is a total pre-estimated completion time of the federated learning, B denotes a total bandwidth owned by the UAV m, f_i^max denotes a maximum computation frequency of the user i, p_i^max denotes a maximum transmission power of the user i, and, h^min and h^max denote a minimum altitude and a maximum altitude of the UAV m for flying, respectively; under a constraint of a maximum delay allowed by the federated learning, a position of the UAV m (the horizontal position q_m={x,y} and the altitude h), the transmission power p=[p₁, . . . p_Nm] and a computation frequency f=[f₁, . . . f_Nm] of the user i, a transmission bandwidth b=[b₁, . . . b_Nm], transmission time t=[t₁ . . . t_Nm] and the local accuracy η are optimized jointly to minimize the target function; constraints C1 and C2 limit the computation frequency and the transmission power of the user i; a constraint C3 denotes that a total delay of the users that participate in the federated learning is not greater than a preset maximum value; a constraint C4 limits the transmission delay, i.e., a transmission of the model must be completed within specified transmission time, and R_i is the achievable transmission rate of the user i; a constraint C5 limits the position of the UAV m and the distance between the user and the UAV m not greater than the coverage range of the UAV m; a constraint C6 limits a flight altitude range of the UAV m; the constraint C7 indicates that a sum of the bandwidth allocated to all users within the coverage range of the UAV m is not greater than a total bandwidth B; and the constraint C8 specifies a range of constraints on the local training accuracy.

In some embodiment, the S2. solving the optimization problem P includes:

• • S2.1. setting an initial horizontal flight position q_m and a minimum flight altitude h of the UAV m;
  • S2.2. setting an initial user resource allocation decision and an initial local accuracy η within the coverage range of the UAV m, wherein the user resource allocation decision comprises the computation frequency f, the transmission time t, the transmission power P and the transmission bandwidth b;
  • S2.3. solving by the optimization problem P based on h, f, t, p, b, η, to obtain the optimal horizontal position of the UAV m;
  • S2.4. solving by the optimization problem P based on h, f, t, p, b and the optimal horizontal position q_m of the UAV m obtained in the S2.3, to obtain the optimal local accuracy η;
  • S2.5. solving by the optimization problem P based on h, the optimal horizontal position q_m of the UAV m obtained in the S2.3 and the optimal local accuracy η obtained in the S2.4;
  • S2.6. repeating the S2.3 to S2.5 until a target total cost function reaches convergence;
  • S2.7. changing the altitude h of the UAV m based on a minimum change value Δh_min of the altitude h;
  • S2.8. in response to the altitude of the UAV m not greater than a preset maximum altitude, repeating the S2.2 to S2.7 until the altitude of the UAV m is greater than the maximum altitude, obtaining the optimal horizontal position q_m of the UAV m, the optimal local accuracy η, the optimal user resource allocation decision, and the optimal altitude h of the UAV m when the total cost function is minimized.

In some embodiment, the S2.3, solving by the optimization problem P to obtain the optimal horizontal position of the UAV m, includes:

• • the altitude of the UAV m is h, an angle of entrapment is θ, and a radius of coverage of the UAV m is r:
    r=h tan(θ)
  • when h, f, t, p, b, η are determined, optimizing the horizontal position q_m of the UAV m; since optimizing the horizontal position of the UAV m only affects the communication energy consumption of the user i; the optimization problem P is equivalent to an optimization problem P1:

$\underset{q_m}{\min }\sum _{i\in N_m}^{❘N_m❘}{p}_i\frac{s}{R_i};$

• • the constraints are:

$\begin{array}{cc}{t}_i\ge \frac{s}{R_i}& C4\end{array}$
C5:∥q_m−q_i∥₂²≤r²;

• • introducing slack variables β, the optimization problem P1 is equivalent to an optimization problem P2:

$\underset{q_m,\beta }{\min }\stackrel{❘N_m❘}{\sum _{i\in N_m}}{p}_{i}s{\beta }_i;$

• • the constraints are:
    C5: ∥q_m−q_i∥₂²≤r²
    C9: sβ_i≤t_i

$\begin{array}{cc}{b}_i{\log }_2\left(1+\frac{p_i{g}_0}{b_i{N}_0\left({q_m-q_i}_2^2+h^2\right)}\right)\ge \frac{1}{{\beta }_i};& \mathrm{C10}\end{array}$

• • introducing slack variables S_m,i=∥q_m−q_i∥₂², the constraint C10 is expanded at a feasible solution S_m,i⁰=∥q_m⁰−q_i∥₂² using a first-order Taylor expansion:

$b_i{\log }_2\left(1+\frac{p_i{g}_0}{b_i{N}_0\left(S_{m,i}+h^2\right)}\right)\ge \lambda \left(S_{m,i}-S_{m,i}^0\right)+\kappa$ $\lambda =-\frac{b_i{g}_0{p}_i{\log }_2\left(e\right)}{N_0{b}_i\left(S_{m,i}^0+h^2\right)\left(S_{m,i}^0+h^2+\frac{g_0{p}_i}{N_0{b}_i}\right)}$ $\kappa =b_i{\log }_2\left(1+\frac{g_0{p}_i}{N_0{b}_i\left(S_{m,i}^0+h^2\right)}\right);$

• • where, λ, κ denote intermediate variables; the optimization problem P2 is further transformed into an optimization problem P3:

$\underset{q_m,\beta }{\min }\sum _{i\in N_m}^{❘N_m❘}{p}_{i}s{\beta }_i$

• • the constraints are:
    C5:∥q_m−q_i∥₂²≤r²
    C9: sβ_i≤t_i

$\begin{array}{cc}\lambda \left(S_{m,i}-S_{m,i}^0\right)+\kappa \ge \frac{1}{{\beta }_i};& \mathrm{C11}\end{array}$

• • the optimization problem P3 is transformed into a convex problem, which is solved using a successive convex approximation (SCA) method to obtain the optimal horizontal position of the UAV m.

In some embodiment, the S2.4 solving by the optimization problem P to obtain the optimal local accuracy η, includes:

• • when h, q_m, f, t, p, b is determined, the optimization problem P is transformed into an optimization problem P4:

$\underset{\eta }{\min }\frac{{\lambda }_1{\log }_2\left(\frac{1}{\eta }\right)+{\lambda }_2}{\left(1-\eta \right)};$

• • the constraints are:

$\begin{array}{cc}{I}_g\left(t_i+I_l\frac{C_i{D}_i}{f_i}\right)\le T;& \mathrm{C3}\end{array}$
C8: 0≤η≤1

• • wherein

${\lambda }_1=a\sum _{i\in N_m}^{❘N_m❘}\kappa C_i{D}_i{f}_i^2,{\lambda }_2=a\sum _{i\in N_m}^{❘N_m❘}{t}_i{p}_i;$

• • the constraint C3 is equivalent to t_i≤υ(η_i), where

$\upsilon \left(\eta \right)=\frac{1-\eta }{a}T+\frac{C_i{D}_i\log \left(\eta \right)v}{f_i},$
since υ(η) is a convex function, the constraint C3 is transformed into η^min≤η≤η^max, where

${\eta }^{m\mathrm{ax}}=\underset{i\in N_m}{\min }{\eta }_i^{\mathrm{ma}x},{\eta }^{min}=\underset{i\in N_m}{\max }{\eta }_i^{min};$
the optimization problem P4 is transformed into an optimization problem P5:

$\underset{\eta }{\min }\frac{{\lambda }_1\log \left(\frac{1}{\eta }\right)+{\lambda }_2}{\left(1-\eta \right)};$

• • the constraints are:
    C12: η^min≤η≤η^max;
  • solving the optimization problem P5 is equivalent to finding roots of a nonlinear function

$H\left(\zeta \right)=\underset{{\eta }^{\min }\le \eta \le {\eta }^{\max }}{\min }{\lambda }_1\log \left(1/\eta \right)+{\lambda }_2-\zeta \left(1-\eta \right),$

which is solved by using a Dinkelbach Method method.

In some embodiment, the S2.5 solving by the optimization problem P to obtain the optimal user resource allocation decision, includes:

• • when q_m, h and η are determined, optimizing f, t, p and b, and the optimization problem P is transformed into an optimization problem P6:

$\underset{f,t,p,b}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D}_i{f}_i^2+p_i{t}_i\right);$

• • the constraints are:
    C1: 0≤f_i≤f_i^max
    C2: 0≤p_i≤p_i^max

$\begin{array}{cc}{I}_g\left(t_i+I_l\frac{C_i{D}_i}{f_i}\right)\le T& \mathrm{C3}\end{array}$ $\begin{array}{cc}{t}_i\ge \frac{s}{R_i}& \mathrm{C4}\end{array}$ $\begin{array}{cc}\sum _{i\in N_m}^{❘N_m❘}{b}_i\le B,b_i>0;& \mathrm{C7}\end{array}$

• • the optimization problem P6 is split into two optimization subproblems;
  • a first subproblem, denoted as subproblem P6-1, is to solve remaining variables f, t and P of the optimization problem P6 under the transmission bandwidth b given:

$\underset{f,t,p}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D}_i{f}_i^2+p_i{t}_i\right);$

• • the constraints are:
    C1: 0≤f_i≤f_i^max
    C2: 0≤p_i≤p_i^max

$\begin{array}{cc}{I}_g\left(t_i+I_l\frac{C_i{D}_i}{f_i}\right)\le T& \mathrm{C3}\end{array}$ $\begin{array}{cc}{t}_i\ge \frac{s}{R_i};& \mathrm{C4}\end{array}$

$f_i=\frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i}$
and

$p_i=\frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i{p}_i}}-1\right)$
are obtained according to the constraints C3, C4, and then are brought into the constraints C1, C2, and subproblem P6-1 is transformed into an optimization problem P7:

$\underset{f,t,p}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D_i\left(\frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i^{*}}\right)}^2+\frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i^{*}{b}_i}}-1\right)t_i^{*}\right);$

• • the constraints are:

$\begin{array}{cc}0\le \frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i}\le f_i^{\max }& \mathrm{C13}\end{array}$ $\begin{array}{cc}0\le \frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i{b}_i}}-1\right)\le p_i^{\max };& \mathrm{C14}\end{array}$

• • a maximum value and a minimum value of t_i are obtained from constraints C13 and C14; the optimization problem P7 is further transformed into an optimization problem P8:

$\underset{t}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D_i\left(\frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i}\right)}^2+\frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i{b}_i}}-1\right)t_i\right);$

• • the constraints are:
    C15: t_i^min≤t_i≤t_i^max;
  • according to the optimization problem P8, when t_i is satisfied

$❘\frac{\partial E_i^{\mathrm{comm}}}{\partial t_i}❘=❘\frac{\partial E_i^{\mathrm{comp}}}{\partial t_i}❘,$
it is an optimal solution t_i*, which is obtained using a bisection method, and f_i* and p_i* are further obtained;

• • the second subproblem, denoted as subproblem P6-2, is to solve the transmission bandwidth b of the optimization problem under variables f, t, p given:

$\underset{b}{\min }\sum _{i\in N_m}^{❘N_m❘}\frac{b_i{t}_i{N}_0}{g_i}\left(2^{\frac{s}{t_i{b}_i}}-1\right);$

• • the constraints are:

$\begin{array}{cc}\sum _{i\in N_m}^{❘N_m❘}{b}_i\le B,b_i>0;& \mathrm{C7}\end{array}$

• • since the optimization problem P8 is convex, an optimal expression of b is obtained by solving using the KKT condition;
  • optimizing the subproblem P6-2 leads to a change in bandwidth b, which in turn affects f, t, p, in the subproblem P6-1, and iteratively solves the subproblem P6-1 and subproblem P6-2 are solved by iteration to obtain the optimal f, t, p and b.

A second aspect, the present application provides an UAV-assisted federated learning resource allocation device, including a processor and a storage medium;

• • wherein the storage medium is configured to store instructions;
  • the processor for operating in accordance with the instructions to perform the method according to the first aspect.

A third aspect, the present application provides a storage medium having a computer program stored thereon, wherein the computer program is executed by the processor to implement the method according to the first aspect.

A fourth aspect, the present application provides a computing device, including:

• • one or more processors, one or more memories, and one or more programs, wherein the one or more programs are stored in the one or more memories and configured to be executed by the one or more processors, wherein the one or more programs includes instructions for executing the method according to the method of the first aspect.

Advantages of the present application over the related art include:

• • 1. The present application, for an UAV-assisted federated learning wireless network scenario, takes into account the influence of the altitude of the UAV m on the coverage range, and jointly considers defining the inverse of the total energy consumption of the user and the number of participating users as the cost function of the system.
  • 2. The present application jointly considers the learning performance and the interests of the user in the process of federated learning, and reduces the user energy consumption while safeguarding the performance of federated learning by jointly optimizing the position of the UAV m (horizontal position and altitude), the transmission power of the user, the computation frequency, the transmission bandwidth, the transmission time, and the local accuracy.
  • 3. Unlike the federated learning methods in traditional scenarios, the method makes full use of the mobility of the UAV m, and achieves a balanced optimization of the user's energy consumption and the federated learning performance by optimizing the horizontal position and altitude of the UAV m.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart according to embodiments of the present application.

FIG. 2 is a schematic diagram of a system model according to embodiments of the present application.

FIG. 3 is a flowchart according to embodiments of the present application.

FIG. 4 is a flowchart according to embodiments of the present application.

FIG. 5 is a flowchart according to embodiments of the present application.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present application is further described below in conjunction with the accompanying drawings. The following embodiments are only used to illustrate the technical solution of the present application more clearly, and cannot be used to limit the scope of the present application.

In the description of the present application, reference is made to the terms “an embodiment”, “some embodiments”, “schematic embodiment”, “example”, “specific example” and “some examples”, means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable way.

First Embodiment

As shown in FIGS. 1 and 3-5, a UAV-assisted federated learning resource allocation method includes:

• • S1. determining a total cost function and constraints of a system based on total energy consumption of users that participate in the federated learning and an inverse of a number of the users, and constructing an optimization problem P with a minimization of the total cost function;
  • S2. solving by the optimization problem P to obtain an optimal horizontal position q_m of the UAV m, an optimal local accuracy η, an optimal user resource allocation decision, and an optimal altitude h of the UAV m.

In some embodiment, the S2. solving the optimization problem P includes:

• • S2.1. setting an initial horizontal flight position q_m and a minimum flight altitude h of the UAV m;
  • S2.2. setting an initial user resource allocation decision and an initial local accuracy η within the coverage range of the UAV m, wherein the user resource allocation decision comprises the computation frequency f, the transmission time t, the transmission power p and the transmission bandwidth b;
  • S2.3. solving by the optimization problem P based on h, f, t, p, b, η, to obtain the optimal horizontal position of the UAV m;
  • S2.4. solving by the optimization problem P based on h, f, t, p, b and the optimal horizontal position q_m of the UAV m obtained in the S2.3, to obtain the optimal local accuracy η;
  • S2.5. solving by the optimization problem P based on h, the optimal horizontal position q_m of the UAV m obtained in the S2.3 and the optimal local accuracy η obtained in the S2.4;
  • S2.6. repeating the S2.3 to S2.5 until a target total cost function reaches convergence;
  • S2.7. changing the altitude h of the UAV m based on a minimum change value Δh_min of the altitude h;
  • S2.8. in response to the altitude of the UAV m not greater than a preset maximum altitude, repeating the S2.2 to S2.7 until the altitude of the UAV m is greater than the maximum altitude, obtaining the optimal horizontal position q_m of the UAV m, the optimal local accuracy η, the optimal user resource allocation decision, and the optimal altitude h of the UAV m when the total cost function is minimized.
  • S3. the UAV m flying to the optimal horizontal position q_m and the optimal altitude h of the UAV m, and the users determine to participate in the federated learning within a coverage range of the UAV m based on the optimal user resource allocation decision and the optimal local accuracy η.

In some embodiment, the S1, constructing the optimization problem P for minimizing the total cost function, includes:

• • S11. a set of users is denoted as N=={1, 2 . . . N}, a set of the users within the coverage range of the UAV m is denoted as N_m; a distance between the user i and the UAV m is:
    d_im=√{square root over (h²+∥q_m−q_i∥₂²)};
  • where h denotes the altitude of the UAV m, q_m={x_m,y_m} denotes a horizontal position of the UAV m, q_i={x_i,y_i} denotes a position of the user i, and a channel gain of the user i is:

$g_i={g_0\left(\frac{d_{\mathrm{im}}}{d_0}\right)}^{-\alpha };$

• • where g₀ is a channel interference power at time d₀=1 m and α is a path loss exponent;
  • S12. energy consumption of the user's terminal during the federated learning comprises training energy and communication energy;
  • S13. D_i denotes an amount of data of the user, f_i denotes a number of revolutions per second of a CPU of the user i, C_i denotes a number of revolutions of the CPU of the user i to process a sample data, and I_l denotes a number of rounds of local training when a local accuracy is achieved η;

$I_l=\frac{2}{\left(2-L\delta \right)\delta y}\log \left(\frac{1}{\eta }\right);$

• • wherein L, γ are relevant parameters about a neural network loss function, δ is a training learning step of the federated learning;
  • training energy consumption E_i^comp of the user i in one iteration of the federated learning is denoted as:
    E_i^comp=κI_lC_iD_if_i²;
  • S14. after the user i completes the local training, a trained model is uploaded to the UAV m by a frequency division multiple access (FDMA); b_i denotes a bandwidth allocated to the user i, p_i denotes a transmission power of the user i, N₀ denotes a noise power spectral density, and according to a Shannon's formula, an achievable transmission rate R_i of the user i is:

$R_i=b_i{\log }_2\left(1+\frac{g_i{p}_i}{N_0{b}_i}\right);$

• • assuming that a size of data of the neural network model w is s and communication energy consumption E_i^comm of the user i is:

$E_i^{\mathrm{comm}}=p_i{t}_i=p_i\frac{s}{b_i{\log }_2\left(1+\frac{g_i{p}_i}{N_0{b}_i}\right)};$

• • S15. when a global model accuracy is required to be achieved ε₀, a number of communication rounds I_g is:

$I_g=\frac{2L^2}{{\gamma }^2\xi }\log \frac{1}{{\epsilon }_0}\frac{1}{1-\eta };$

• • where ξ denotes relevant parameters in a local neural network training, a total energy consumption E^total of a whole federated learning process is:

$E^{\mathrm{total}}=I_g\sum _{i\in N_m}^{❘N_m❘}\left(E_i^{\mathrm{comm}}+E_i^{\mathrm{comp}}\right);$

• • S16. Considering that the user's battery capacity is limited and the energy consumption of the terminal device directly affects the user's experience, the total energy consumption of the user is defined as part of the cost function. Since the performance of federated learning is related to the number of participating users, the more the number of participating users, the faster the learning convergence will be, and the more the data diversity of the participating users, the better the generalisation ability of the model obtained, so the inverse of the number of participating users is defined as the other part of the cost function, which indicates the performance of federated learning. In order to achieve a balance between the energy consumption of users and the performance of federated learning, the total cost function C is defined as:

$C=E_{\mathrm{total}}+\rho \frac{1}{N_m};$

• • a target function is:

$\underset{q_m,h,f,t,p,b,\eta }{\min }C=\underset{q_m,h,f,t,p,b,\eta }{\min }\frac{a}{\left(1-\eta \right)}\left(\sum _{i\in N_m}^{❘N_m❘}\log \left(\frac{1}{\eta }\right)v{C}_i{D}_i{f}_i^2+t_i{p}_i\right)+\frac{\rho }{N_m};$

• • wherein

$a=\frac{2L^2}{I^2\zeta }\log \frac{1}{{\epsilon }_0}$
and

$v=\frac{2}{\left(2-L\delta \right)\mathrm{\delta \gamma }}$
denote fixed values and ρ denotes a weighting factor;

• • S17. considering the total energy consumption of the users and a performance of federated learning, the optimization problem P of the system is:

$\underset{q_m,h,f,t,p,b,\eta }{\min }\frac{a}{\left(1-\eta \right)}\left(\sum _{j\in N_m}^{\left|N_m\right|}\log \left(\frac{1}{\eta }\right)v{C}_i{D}_i{f}_i^2+t_i{p}_i\right)+\frac{\rho }{N_m};$

• • the constraints are:
    C1: 0≤f_i≤f_i^max
    C2: 0≤p_i≤p_i^max

$\begin{array}{cc}{I}_g\left(t_i+I_i\frac{C_i{D}_i}{f_i}\right)\le T& \mathrm{C3}\end{array}$ $\begin{array}{cc}{t}_i\ge \frac{s}{R_i}& \mathrm{C4}\end{array}$
C5: ∥q_m−q_i∥₂²≤r²
C6: h^min≤h≤h^max

$\begin{array}{cc}\sum _{l\in N_m}^{\left|N_m\right|}{b}_i\le B,b_i>0& \mathrm{C7}\end{array}$

As shown in FIG. 2, where T is a total pre-estimated completion time of the federated learning, B denotes a total bandwidth owned by the UAV m, f_i^max denotes a maximum computation frequency of the user i, p_i^max denotes a maximum transmission power of the user i, and, h^min and h^max denote a minimum altitude and a maximum altitude of the UAV m for flying, respectively; under a constraint of a maximum delay allowed by the federated learning, a position of the UAV m (the horizontal position q_m={x,y} and the altitude h), the transmission power p=[p₁, . . . p_Nm] and a computation frequency f=[f₁, . . . f_Nm] of the user i, a transmission bandwidth b=[b₁, . . . b_Nm], transmission time t=[t₁, . . . t_Nm] and the local accuracy η are optimized jointly to minimize the target function; constraints C1 and C2 limit the computation frequency and the transmission power of the user i; a constraint C3 denotes that a total delay of the users that participate in the federated learning is not greater than a preset maximum value; a constraint C4 limits the transmission delay, i.e., a transmission of the model must be completed within specified transmission time, and R_i is the achievable transmission rate of the user i; a constraint C5 limits the position of the UAV m and the distance between the user and the UAV m not greater than the coverage range of the UAV m; a constraint C6 limits a flight altitude range of the UAV m, too low the altitude results in too few participating users, and too high the altitude results in a shortage of wireless resources, leading to a rise in delay when learning energy, both of which will slow down the convergence of federated learning; the constraint C7 indicates that a sum of the bandwidth allocated to all users within the coverage range of the UAV m is not greater than a total bandwidth B; and the constraint C8 specifies a range of constraints on the local training accuracy η.

An embodiment of the present application provides an UAV-assisted federated learning resource allocation method, in which the optimal resource allocation decision is obtained sequentially by successive convex approximation, Dinkelbach Method method, dichotomy method with KKT condition, so as to motivate more users to join the federated learning.

In some embodiment, the S2.3, solving by the optimization problem P to obtain the optimal horizontal position q_m of the UAV m, includes:

• • the altitude of the UAV m is h, an angle of entrapment is θ, and a radius of coverage of the UAV m is r:
    r=h tan(θ);
  • when h, f, t, p, b, η are determined, optimizing the horizontal position q_m of the UAV m; since optimizing the horizontal position of the UAV m only affects the communication energy consumption of the user i; the optimization problem P is equivalent to an optimization problem P1:

$\underset{q_m}{\min }\underset{i\in N_m}{\sum ^{|N_m❘}}{p}_i\frac{s}{R_i};$

• • the constraints are:

$\begin{array}{cc}{t}_i\ge \frac{s}{R_i}& \mathrm{C4}\end{array}$
C5: ∥q_m−q_i∥₂²≤r²;

• • introducing slack variables β, the optimization problem P1 is equivalent to an optimization problem P2:

$\underset{q_m,\beta }{\min }\underset{i\in N_m}{\sum ^{|N_m❘}}{p}_{i}s{\beta }_i;$

• • the constraints are:
    C5: ∥q_m−q_i∥₂²≤r²
    C9:sβ_i≤t_i

$\begin{array}{cc}{b}_i{\log }_2\left(1+\frac{p_i{g}_0}{b_i{N}_0\left({q_m-q_i}_2^2+h^2\right)}\right)\ge \frac{1}{{\beta }_i};& \mathrm{C10}\end{array}$

• • introducing slack variables S_m,i=∥q_m−q_i∥₂², the constraint C10 is expanded at a feasible solution S_m,i⁰=∥q_m⁰−q_i∥₂² using a first-order Taylor expansion:

$b_i{\log }_2\left(1+\frac{p_i{g}_0}{b_i{N}_0\left(S_{m,i}+h^2\right)}\right)\ge \lambda \left(S_{m,i}-S_{m,i}^0\right)+\kappa$

$\lambda =-\frac{b_i{g}_0{p}_i{\log }_2\left(e\right)}{N_0{b}_i\left(S_{m,i}^0+h^2\right)\left(S_{m,i}^0+h^2+\frac{g_0{p}_i}{N_0{b}_i}\right)}$

$\kappa =b_i{\log }_2\left(1+\frac{g_0{p}_1}{N_0{b}_i\left(S_{m,i}^0+h^2\right)}\right);$

• • where, λ, κ denote intermediate variables; the optimization problem P2 is further transformed into an optimization problem P3:

$\underset{q_m,\beta }{\min }\underset{i\in N_m}{\sum ^{|N_m❘}}{p}_{i}s{\beta }_i$

• • the constraints are:
    C5: ∥q_m−q_i∥₂²≤r²
    C9:sβ_i≤t_i

$\begin{array}{cc}\lambda \left(S_{m,i}-S_{m,i}^0\right)+\kappa \ge \frac{1}{{\beta }_i};& \mathrm{C11}\end{array}$

• • the optimization problem P3 is transformed into a convex problem, which is solved using a successive convex approximation (SCA) method to obtain the optimal horizontal position of the UAV m.

When the UAV m arrives at the new position, the coverage position of the UAV changes, and due to the constraint C5, the original user is still within the range of the UAV m, but a new user may join, at this time, the values of the variables are re-initialised and the algorithm is re-iterated.

In some embodiment, the S2.4 solving by the optimization problem P to obtain the optimal local accuracy η includes:

• • when h, q_m, f, t, p, b is determined, the optimization problem P is transformed into an optimization problem P4:

$\underset{\eta }{\min }\frac{{\lambda }_1{\log }_2\left(\frac{1}{\eta }\right)+{\lambda }_2}{\left(1-\eta \right)};$

• • the constraints are:

$\begin{array}{cc}{I}_g\left(t_i+I_l\frac{C_i{D}_i}{f_i}\right)\le T;& C3\end{array}$
C8: 0≤η≤1

• • wherein

${\lambda }_1=a\sum _{i\in N_m}^{❘N_m❘}\kappa C_i{D}_i{f}_i^2,{\lambda }_2=a\sum _{i\in N_m}^{❘N_m❘}{t}_i{p}_i;$

• • the constraint C3 is equivalent to t_i≤υ(η_i), where

$\upsilon \left(\eta \right)=\frac{1-\eta }{a}T+\frac{C_i{D}_i\log \left(\eta \right)v}{f_i},$

• • since υ(η) is a convex function, the constraint C3 is transformed into η^min≤η≤η^max, where

${\eta }^{\max }=\underset{i\in N_m}{\min }{\eta }_i^{\max },{\eta }^{\min }=\underset{i\in N_m}{\max }{\eta }_i^{\min };$

• •  the optimization problem P4 is transformed into an optimization problem P5:

$\underset{\eta }{\min }\frac{{\lambda }_1\log \left(\frac{1}{\eta }\right)+{\lambda }_2}{\left(1-\eta \right)};$

• • the constraints are:
    C12: η^min≤η≤η^max;
  • solving the optimization problem P5 is equivalent to finding roots of a nonlinear function

$H\left(\zeta \right)=\underset{{\eta }^{\min }\le \eta \le {\eta }^{\max }}{\min }{\lambda }_1\log \left(1/\eta \right)+{\lambda }_2-\zeta \left(1-\eta \right),$

• •  which is solved by using a Dinkelbach Method method.

In some embodiment, the S2.5 solving by the optimization problem P to obtain the optimal user resource allocation decision, includes:

• • when q_m, h and η are determined, optimizing f, t, p and b, and the optimization problem P is transformed into an optimization problem P6:

$\underset{f,t,p,b}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D}_i{f}_i^2+p_i{t}_i\right);$

• • the constraints are:
    C1: 0≤f_i≤f_i^max
    C2: 0≤p_i≤p_i^max

$\begin{array}{cc}{I}_g\left(t_i+I_l\frac{C_i{D}_i}{f_i}\right)\le T& C3\end{array}$ $\begin{array}{cc}{t}_i\ge \frac{s}{R_i}& C4\end{array}$ $\begin{array}{cc}\sum _{i\in N_m}^{❘N_m❘}{b}_i\le B,b_i>0;& C7\end{array}$

• • the optimization problem P6 is split into two optimization subproblems;
  • a first subproblem, denoted as subproblem P6-1, is to solve remaining variables f, t and P of the optimization problem P6 under the transmission bandwidth b given:

$\underset{f,t,p}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D}_i{f}_i^2+p_i{t}_i\right);$

• • the constraints are:
    C1: 0≤f_i≤f_i^max
    C2: 0≤p_i≤p_i^max

$\begin{array}{cc}{I}_g\left(t_i+I_l\frac{C_i{D}_i}{f_i}\right)\le T;& C3\end{array}$ $\begin{array}{cc}{t}_i\ge \frac{s}{R_i};& C4\end{array}$

$f_i=\frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i}$
and

$p_i=\frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i{b}_i}}-1\right)$
are obtained according to the constraints C3, C4, and then are brought into the constraints C1, C2, and subproblem P6-1 is transformed into an optimization problem P7:

$\underset{f,t,p}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D_i\left(\frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i^{*}}\right)}^2+\frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i^{*}{b}_i}}-1\right)t_i^{*}\right);$

• • the constraints are:

$\begin{array}{cc}0\le \frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i}\le f_i^{\max }& C13\end{array}$ $\begin{array}{cc}0\le \frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i{b}_i}}-1\right)\le p_i^{\max };& C14\end{array}$

a maximum value and a minimum value of t_i are obtained from constraints C13 and C14; the optimization problem P7 is further transformed into an optimization problem P8:

$\underset{t}{\min }\frac{a}{\left(1-\eta \right)}\sum _{i\in N_m}^{❘N_m❘}\left(v\log \left(\frac{1}{\eta }\right)C_i{D_i\left(\frac{I_l{C}_i{D}_i}{\frac{T}{I_g}-t_i}\right)}^2+\frac{N_0{b}_i}{g_i}\left(2^{\frac{s}{t_i{b}_i}}-1\right)t_i\right);$

• • the constraints are:
    C15: t_i^min≤t_i≤t_i^max;
  • according to the optimization problem P8, when t_i is satisfied

$❘\frac{\partial E_i^{comm}}{\partial t_i}❘=❘\frac{\partial E_i^{comp}}{\partial t_i}❘,$
it is an optimal solution t_i*, which is obtained using a bisection method, and f_i* and p_i* are further obtained;

• • the second subproblem, denoted as subproblem P6-2, is to solve the transmission bandwidth b of the optimization problem under variables f, t, p given:

$\underset{b}{\min }\sum _{i\in N_m}^{\left|N_m\right|}\frac{b_i{t}_i{N}_0}{g_i}\left(2^{\frac{s}{t_i{b}_i}}-1\right);$

• • the constraints are:

$\begin{array}{cc}\sum _{l\in N_m}^{\left|N_m\right|}{b}_i\le B,b_i>0;& C7\end{array}$

• • since the optimization problem P8 is convex, an optimal expression of b is obtained by solving using the KKT condition;
  • optimizing the subproblem P6-2 leads to a change in bandwidth b, which in turn affects f, t, p, in the subproblem P6-1, and iteratively solves the subproblem P6-1 and subproblem P6-2 are solved by iteration to obtain the optimal f, t, p and b.

Second Embodiment

In a second aspect, the present application provides an UAV-assisted federated learning resource allocation device, including a processor and a storage medium;

• • wherein the storage medium is configured to store instructions;
  • the processor for operating in accordance with the instructions to perform the method according to the first embodiment.

Third Embodiment

In a third aspect, the present application provides a storage medium having a computer program stored thereon, wherein the computer program is executed by the processor to implement the method according to the first embodiment.

Fourth Embodiment

In a fourth aspect, the present application provides a computing device, including:

• • one or more processors, one or more memories, and one or more programs, wherein the one or more programs are stored in the one or more memories and configured to be executed by the one or more processors, wherein the one or more programs includes instructions for executing the method according to the method of the first embodiment.

It should be appreciated by those skilled in the art that embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of a fully hardware embodiment, a fully software embodiment, or an embodiment that combines software and hardware aspects. Further, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk memory, CD-ROM, optical memory, and the like) that contain computer-usable program code therein.

The present application is described with reference to flowcharts and/or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present application. It should be understood that each of the processes and/or boxes in the flowchart and/or block diagram, and the combination of processes and/or boxes in the flowchart and/or block diagram, may be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data-processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data-processing device produce a device for carrying out the functions specified in the one process or multiple processes of the flowchart and/or the one box or multiple boxes of the box diagram.

These computer program instructions may also be stored in computer-readable memory capable of directing the computer or other programmable data processing device to operate in a particular manner such that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device that implements the function specified in the flowchart one process or a plurality of processes and/or one box or a plurality of boxes.

These computer program instructions may also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are performed on the computer or other programmable device to produce computer-implemented processing, such that the instructions executed on the computer or other programmable device provide steps for implementing the functionality specified one process or a plurality of processes in the flowchart and/or the box diagram one box or a plurality of boxes in the box diag.

The above embodiments of the present application are described in detail in connection with the accompanying drawings, but the present application is not limited to the above embodiments, and various variations may be made within the scope of knowledge possessed by those skilled in the art without departing from the purposes of the present application.

Claims

1. A method of allocating resource by UAV-assisted federated learning, applied on an environment comprising a unmanned aerial vehicle (UAV) and user devices, and the UAV as an airborne base station is combined with federated learning, comprising: g i = g 0 ( d im d 0 ) - α; I l = 2 ( 2 - L ⁢ δ ) ⁢ δ ⁢ y ⁢ log ⁡ ( 1 η ); R i = b i ⁢ log 2 ( 1 + g i ⁢ p i N 0 ⁢ b i ); E i comm = p i ⁢ t i = p i ⁢ s b i ⁢ log 2 ( 1 + g i ⁢ p i N 0 ⁢ b i ); I g = 2 ⁢ L 2 γ 2 ⁢ ξ ⁢ log ⁢ 1 ε 0 ⁢ 1 1 - η; E total = I g ⁢ ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" ( E i comm + E i comp ); C = E total + ρ ⁢ 1 N m; min q m, h, f, t, p, n, η C = min q m, h, f, t, p, b, η a ( 1 - η ) ⁢ ( ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" log ⁡ ( 1 η ) ⁢ vC i ⁢ D i ⁢ f i 2 + t i ⁢ p i ) + ρ N m; a = 2 ⁢ L 2 γ 2 ⁢ ζ ⁢ log ⁢ 1 ε 0 v = 2 ( 2 - L ⁢ δ ) ⁢ δγ min q m, h, f, t, p, b, η a ( 1 - η ) ⁢ ( ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" log ⁡ ( 1 η ) ⁢ vC i ⁢ D i ⁢ f i 2 + t i ⁢ p i ) + ρ N m; 0 ≤ f i ≤ f i max C ⁢ 1 0 ≤ p i ≤ p i max C ⁢ 2 I g ( t i + I l ⁢ C i ⁢ D i f i ) ≤ T C ⁢ 3 t i ≥ s R i C ⁢ 4  q m - q i  2 2 ≤ r 2 C ⁢ 5 h min ≤ h ≤ h max C ⁢ 6 ∑ i ∈ N m | N m | b i ≤ B, b i > 0 C ⁢ 7 0 ≤ η ≤ 1; C ⁢ 8

S1. determining a total cost function and constraints of a system based on total energy consumption of user devices that participate in the federated learning and an inverse of a number of the user devices, and constructing an optimization problem P with a minimization of the total cost function;

S2. solving by the optimization problem P to obtain an optimal horizontal position of the (UAV), an optimal local accuracy, an optimal user resource allocation decision, and an optimal altitude of the UAV; and

S3. controlling the UAV to fly to the optimal horizontal position and the optimal altitude of the UAV, and the user devices within a coverage range of the UAV determining to participate in the federated learning based on the optimal user resource allocation decision and the optimal local accuracy to upload neural network model parameters related to the data, and

a main server securely aggregating the neural network model parameters and feed the neural network model parameters back to the user devices within the coverage range of the UAV for updating a global model according to the dataset owned by the user devices within the coverage range of the UAV;

wherein the S1, constructing the optimization problem P for minimizing the total cost function, comprises:

S11. a set of user devices is denoted as N=={1, 2... N}, a set of the user devices within the coverage range of the UAV is denoted as Nm; a distance between the user device i and the UAV is: dim=√{square root over (h2+∥qm−qi∥22)};

where h denotes the altitude of the UAV, qm={xm,ym} denotes a horizontal position of the UAV, qi={xi,yi} denotes a position of the user device i, and a channel gain of the user device i is:

where g0 is a channel interference power at timed d0=1 m and α is a path loss exponent;

S12. energy consumption of the user device during the federated learning comprises training energy and communication energy;

S13. Di denotes an amount of data of the user device, fi denotes a number of revolutions per second of a CPU of the user device i, Ci denotes a number of revolutions of the CPU of the user device i to process a sample data, and Il denotes a number of rounds of local training when a local accuracy is achieved η;

wherein L, γ are relevant parameters about a neural network loss function, δ is a training learning step of the federated learning;

training energy consumption Eicomp of the user device i in one iteration of the federated learning is denoted as: Eicomp=κIlCiDifi2;

S14. after the user completes the local training, a trained model is uploaded to the UAV by a frequency division multiple access (FDMA); bi denotes a bandwidth allocated to the user device i, p, denotes a transmission power of the user device i, N0 denotes a noise power spectral density, and according to a Shannon's formula an achievable transmission rate Ri of the user device i is:

assuming that a size of data of the neural network model w is s and communication energy consumption Eicomp of the user device i is:

S15. when a global model accuracy is required to be achieved ε0 a number of communication rounds Ig is:

where ξ denotes relevant parameters in a local neural network training, a total energy consumption Etotal of a whole federated learning process is:

S16. the total cost function C is defined as:

a target function is:

wherein

 and

 denote fixed values and ρ denotes a weighting factor;

S17. considering the total energy consumption of the user devices and a performance of federated learning, the optimization problem P of the system is:

the constraints are:

where T is a total pre-estimated completion time of the federated learning, B denotes a total bandwidth owned by the UAV, fimax denotes a maximum computation frequency of the user device i, pimax denotes a maximum transmission power of the user device i, and, hmin and hmax denote a minimum altitude and a maximum altitude of the UAV for flying, respectively; under a constraint of a maximum delay allowed by the federated learning, a position of the UAV, the transmission power p=[p1,... pNm] and a computation frequency f=[f1,... fNm] of the user device i, a transmission bandwidth b=[b1,... bNm], transmission time t=[t1... tNm] and the local accuracy η are optimized jointly to minimize the target function; constraints C1 and C2 limit the computation frequency and the transmission power of the user device i; a constraint C3 denotes that a total delay of the user devices that participate in the federated learning is not greater than a preset maximum value; a constraint C4 limits the transmission delay, and Ri is the achievable transmission rate of the user device i; a constraint C5 limits the position of the UAV m and the distance between the user device and the UAV not greater than the coverage range of the UAV; a constraint C6 limits a flight altitude range of the UAV; the constraint C7 indicates that a sum of the bandwidth allocated to all user devices within the coverage range of the UAV is not greater than a total bandwidth B; and the constraint C8 specifies a range of constraints on the local training accuracy.

2. The method of allocating resource by UAV-assisted federated learning according to claim 1,

wherein the S2. solving the optimization problem P comprises: S2.1. setting an initial horizontal flight position qm and a minimum flight altitude h of the UAV; S2.2. setting an initial user resource allocation decision and an initial local accuracy η within the coverage range of the UAV, wherein the user resource allocation decision comprises the computation frequency f, the transmission time t, the transmission power p and the transmission bandwidth b; S2.3. solving by the optimization problem P based on h, f, t, p, b, η, to obtain the optimal horizontal position of the UAV; S2.4. solving by the optimization problem P based on h, f, t, p, b and the optimal horizontal position qm of the UAV obtained in the S2.3, to obtain the optimal local accuracy η; S2.5. solving by the optimization problem P based on h, the optimal horizontal position qm of the UAV obtained in the S2.3 and the optimal local accuracy η obtained in the S2.4; S2.6. repeating the S2.3 to S2.5 until a target total cost function reaches convergence; S2.7. changing the altitude h of the UAV based on a minimum change value Δhmin of the altitude h; S2.8. in response to the altitude of the UAV not greater than a preset maximum altitude, repeating the S2.2 to S2.7 until the altitude of the UAV is greater than the maximum altitude, obtaining the optimal horizontal position qm of the UAV, the optimal local accuracy η, the optimal user resource allocation decision, and the optimal altitude h of the UAV when the total cost function is minimized.

3. The method of allocating resource by UAV-assisted federated learning according to claim 2, wherein the S2.3, solving by the optimization problem P to obtain the optimal horizontal position of the UAV, comprises: min q m ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" p i ⁢ s R i; min q m, β ∑ ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" j ∈ N m p i ⁢ s ⁢ β i; b i ⁢ log 2 ( 1 + p i ⁢ g 0 b i ⁢ N 0 ( ❘ "\[LeftBracketingBar]" q m - q i  2 2 + h 2 ) ) ≥ 1 β i; C10 b i ⁢ log 2 ( 1 + p i ⁢ g 0 b i ⁢ N 0 ( S m, i + h 2 ) ) ≥ λ ⁡ ( S m, i - S m, i 0 ) + κ λ = - b i ⁢ g 0 ⁢ p i ⁢ log 2 ( e ) N 0 ⁢ b i ( S m, i 0 + h 2 ) ⁢ ( S m, i 0 + h 2 + g 0 ⁢ p i N 0 ⁢ b i ) κ = b i ⁢ log 2 ( 1 + g 0 ⁢ p i N 0 ⁢ b i ( S m, i 0 + h 2 ) ); min q m, β ∑ ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" j ∈ N m p i ⁢ s ⁢ β i λ ⁡ ( S m, i - S m, i 0 ) + κ ≥ 1 β i; C11

the altitude of the UAV is h, an angle of entrapment is θ, and a radius of coverage of the UAV is r: r=h tan(θ);

when h, f, t, p, b, q are determined, optimizing the horizontal position qm of the UAV; since optimizing the horizontal position of the UAV only affects the communication energy consumption of the user device i; the optimization problem P is equivalent to an optimization problem P1:

the constraints are: t i ≥ s R i C ⁢ 4 C5: ∥qm−qi∥22≤r2;

introducing slack variables β, the optimization problem P1 is equivalent to an optimization problem P2:

the constraints are: C5: ∥qm−qi∥22≤r2 C9: sβi≤ti

introducing slack variables Sm,i=∥qm−qi∥22, the constraint C10 is expanded at a feasible solution Sm,i0=∥qm0−qi∥22 using a first-order Taylor expansion:

where, λ, κ denote intermediate variables; the optimization problem P2 is further transformed into an optimization problem P3:

the constraints are: C5: ∥qm−qi∥22≤r2 C9: sβi≤ti

the optimization problem P3 is transformed into a convex problem, which is solved using a successive convex approximation (SCA) method to obtain the optimal horizontal position of the UAV.

4. The method of allocating resource by UAV-assisted federated learning according to claim 2, wherein the S2.4 solving by the optimization problem P to obtain the optimal local accuracy η, comprises: min η A 1 ⁢ log 2 ( 1 η ) + λ 2 ( 1 - η ); λ 1 = a ⁢ ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" κ ⁢ C i ⁢ D i ⁢ f i 2, λ 2 = a ⁢ ∑ i ∈ N m ❘ "\[LeftBracketingBar]" V m ❘ "\[RightBracketingBar]" t i ⁢ p i; υ ⁡ ( η ) = 1 - η a ⁢ T + C i ⁢ D i ⁢ log ⁡ ( η ) ⁢ v f i, η max = min i ∈ N m η i max, η min = max i ∈ N m η i min; min η λ 1 ⁢ log ⁡ ( 1 η ) + λ 2 ( 1 - η ); H ⁡ ( ζ ) = min η m ⁢ i ⁢ n ≤ η ≤ η ma ⁢ x λ 1 ⁢ log ⁡ ( 1 / η ) + λ 2 - ζ ⁡ ( 1 - η ), which is solved by using a Dinkelbach Method method.

when h, qm, f, t, p, b is determined, the optimization problem P is transformed into an optimization problem P4:

the constraints are: I g ( t i + I i ⁢ C i ⁢ D i f i ) ≤ T; C3 C8:0≤η≤1

wherein

the constraint C3 is equivalent to ti≤υ(ηi), where

since υ(η) is a convex function, the constraint C3 is transformed into ηmin≤η≤ηmax, where

 the optimization problem P4 is transformed into an optimization problem P5:

the constraints are: C12: ηmin≤η≤ηmax;

solving the optimization problem P5 is equivalent to finding roots of a nonlinear function

5. The method of allocating resource by UAV-assisted federated learning according to claim 2, wherein the S2.5 solving by the optimization problem P to obtain the optimal user resource allocation decision, comprises: min f, t, p, b a ( 1 - η ) ⁢ ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" ( v ⁢ log ⁡ ( 1 η ) ⁢ C i ⁢ D i ⁢ f i 2 + p i ⁢ t i ); I g ( t i + I l ⁢   C i ⁢ D i f i ) ≤ T C ⁢ 3 t i ≥ s R i C ⁢ 4 ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" b i ≤ B, b i > 0; C ⁢ 7 min f, t, p a ( 1 - η ) ⁢ ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" ( v ⁢ log ⁡ ( 1 η ) ⁢ C i ⁢ D i ⁢ f i 2 + p i ⁢ t i ); I g ( t i + I l ⁢   C i ⁢ D i f i ) ≤ T C ⁢ 3 t i ≥ s R i; C ⁢ 4 f i = I l ⁢ C i ⁢ D i T I g - t i ⁢ and ⁢ p i = N 0 ⁢ b i g i ⁢ ( 2 s t i ⁢ b i - 1 ) min f, t, p a ( 1 - η ) ⁢ ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" ( v ⁢ log ⁡ ( 1 η ) ⁢ C i ⁢ D i ( I l ⁢ C i ⁢ D i T I g - t i * ) 2 + N 0 ⁢ b i g i ⁢ ( 2 s t i * ⁢ b i - 1 ) ⁢ t i * ); 0 ≤ I t ⁢ C i ⁢ D i T I g - t i ≤ f i max C ⁢ 13 0 ≤ N 0 ⁢ b i g i ⁢ ( 2 s t i ⁢ b i - 1 ) ≤ p i max; C ⁢ 14 min t a ( 1 - η ) ⁢ ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" ( v ⁢ log ⁡ ( 1 η ) ⁢ C i ⁢ D i ( I l ⁢ C i ⁢ D i T I g - t i ) 2 + N 0 ⁢ b g i ⁢ ( 2 s t i ⁢ b i - 1 ) ⁢ t i ); ❘ "\[LeftBracketingBar]" ∂ E i c ⁢ o ⁢ m ⁢ m ∂ t i ❘ "\[RightBracketingBar]" = ❘ "\[LeftBracketingBar]" ∂ E i comp ∂ t i ❘ "\[RightBracketingBar]", min b ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" b i ⁢ t i ⁢ N 0 g i ⁢ ( 2 s t i ⁢ b i - 1 ); ∑ i ∈ N m ❘ "\[LeftBracketingBar]" N m ❘ "\[RightBracketingBar]" b i ≤ B, b i > 0; C ⁢ 7

when qm, h and η are determined, optimizing f, t, p and b, and the optimization problem P is transformed into an optimization problem P6:

the constraints are: C1: 0≤fi≤fimax C2: 0≤pi≤pimax

the optimization problem P6 is split into two optimization subproblems;

a first subproblem, denoted as subproblem P6-1, is to solve remaining variables f, t and p of the optimization problem P6 under the transmission bandwidth b given:

the constraints are: C1: 0≤fi≤fimax C2: 0≤pi≤pimax

 are obtained according to the constraints C3, C4, and then are brought into the constraints C1, C2, and subproblem P6-1 is transformed into an optimization problem P7:

the constraints are:

a maximum value and a minimum value of ti are obtained from constraints C13 and C14; the optimization problem P7 is further transformed into an optimization problem P8:

the constraints are: C15: timin≤ti≤timax;

according to the optimization problem P8, when t is satisfied

 it is an optimal solution ti*, which is obtained using a bisection method, and fi* and pi* are further obtained;

the second subproblem, denoted as subproblem P6-2, is to solve the transmission bandwidth b of the optimization problem under variables f, t, p given:

the constraints are:

since the optimization problem P8 is convex, an optimal expression of b is obtained by solving using the KKT condition;

optimizing the subproblem P6-2 leads to a change in bandwidth b, which in turn affects f, t, p, in the subproblem P6-1, and iteratively solves the subproblem P6-1 and subproblem P6-2 are solved by iteration to obtain the optimal f, t, p and b.

6. A device of allocating resource by UAV-assisted federated learning, comprising a processor and a storage medium;

wherein the storage medium is configured to store instructions;

the processor for operating in accordance with the instructions to perform the method according to claim 1.

7. A storage medium having a computer program stored thereon, wherein the computer program is executed by the processor to implement the method according to claim 1.

8. A computing device, comprising:

one or more processors, one or more memories, and one or more programs, wherein the one or more programs are stored in the one or more memories and configured to be executed by the one or more processors, wherein the one or more programs comprises instructions for executing the method according to claim 1.